Answer
Center of circle is $\left( 0,0 \right)$ and radius is $r=\frac{1}{6}$
Work Step by Step
Standard equation of the circle is:
${{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}}$ (equation - 1)
And equation of circle is $36{{x}^{2}}+36{{y}^{2}}=1$ (equation - 2)
Multiply $\frac{1}{36}$on both the sides of equation $36{{x}^{2}}+36{{y}^{2}}=1$.
$\begin{align}
& 36\times \frac{1}{36}{{x}^{2}}+36\times \frac{1}{36}{{y}^{2}}=\frac{1}{36} \\
& {{x}^{2}}+{{y}^{2}}=\frac{1}{36}
\end{align}$
Now compare the standard equation with equation ${{x}^{2}}+{{y}^{2}}=\frac{1}{36}$.
$\begin{align}
& {{\left( x-0 \right)}^{2}}+{{\left( y-0 \right)}^{2}}=\frac{1}{36} \\
& {{\left( x-0 \right)}^{2}}+{{\left( y-0 \right)}^{2}}={{\left( \frac{1}{6} \right)}^{2}} \\
\end{align}$
Center coordinate of circle is $\left( h=0,k=0 \right)$.
And radius of circle is $r=\frac{1}{6}$.
To graph, we plot the points $\left( 0,0.1667 \right)$, $\left( 0,-0.1667 \right)$, $\left( -0.1667,0 \right)$, and $\left( 0.1667,0 \right)$ which are, respectively, $\frac{1}{6}$ unit above, below, left and right of $\left( 0,0 \right)$.
